Purpose
PDGSRFS improves the computed solution to a system of linear
equations and provides error bounds and backward error estimates
for the solution.
Arguments
n (input) int (global)
The order of the system of linear equations.
A (input) SuperMatrix*
The original matrix A, or the scaled A if equilibration was done.
A is also permuted into diag(R)*A*diag(C)*Pc'. The type of A can be:
Stype = SLU_NR_loc; Dtype = SLU_D; Mtype = SLU_GE.
anorm (input) double
The norm of the original matrix A, or the scaled A if
equilibration was done.
LUstruct (input) LUstruct_t*
The distributed data structures storing L and U factors.
The L and U factors are obtained from pdgstrf for
the possibly scaled and permuted matrix A.
See superlu_ddefs.h for the definition of 'LUstruct_t'.
ScalePermstruct (input) ScalePermstruct_t* (global)
The data structure to store the scaling and permutation vectors
describing the transformations performed to the matrix A.
grid (input) gridinfo_t*
The 2D process mesh. It contains the MPI communicator, the number
of process rows (NPROW), the number of process columns (NPCOL),
and my process rank. It is an input argument to all the
parallel routines.
Grid can be initialized by subroutine SUPERLU_GRIDINIT.
See superlu_defs.h for the definition of 'gridinfo_t'.
B (input) double* (local)
The m_loc-by-NRHS right-hand side matrix of the possibly
equilibrated system. That is, B may be overwritten by diag(R)*B.
ldb (input) int (local)
Leading dimension of matrix B.
X (input/output) double* (local)
On entry, the solution matrix Y, as computed by PDGSTRS, of the
transformed system A1*Y = Pc*Pr*B. where
A1 = Pc*Pr*diag(R)*A*diag(C)*Pc' and Y = Pc*diag(C)^(-1)*X.
On exit, the improved solution matrix Y.
In order to obtain the solution X to the original system,
Y should be permutated by Pc^T, and premultiplied by diag(C)
if DiagScale = COL or BOTH.
This must be done after this routine is called.
ldx (input) int (local)
Leading dimension of matrix X.
nrhs (input) int
Number of right-hand sides.
SOLVEstruct (output) SOLVEstruct_t* (global)
Contains the information for the communication during the
solution phase.
berr (output) double*, dimension (nrhs)
The componentwise relative backward error of each solution
vector X(j) (i.e., the smallest relative change in
any element of A or B that makes X(j) an exact solution).
stat (output) SuperLUStat_t*
Record the statistics about the refinement steps.
See util.h for the definition of SuperLUStat_t.
info (output) int*
= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
Internal Parameters
ITMAX is the maximum number of steps of iterative refinement.